Right now, Son and Dish Chairman Charles Ergen are locked in an intensifying takeover battle for Sprint. Son has an agreement to buy 70% of Sprint for $20.1 billion, but Ergen has lobbed in an unsolicited offer to buy the whole company for $25.5 billion.

Some analysts have speculated that should Son prevail in the fight for Sprint, Ergen’s consolation prize could be a “spectrum-hosting” arrangement in which Sprint’s cellphone towers are used to provide service over Ergen’s airwaves. A deal could let Ergen put his spectrum to use and accomplish his long-sought goal of getting into the wireless business.

In an interview Tuesday, Son emphasized that he was focused on closing his deal for Sprint. But he signaled a willingness to deal with Ergen down the road.

“If he wants to utilize his frequencies and ask for some kind of partnership with us hosting his frequencies, spectrum, as one new business offer, I could think about the potential opportunity,” Son said in response to a question about such a network deal. “I don’t want to complicate the deal structure right now or delay any of the offer that we are supposed to close on July 1.”

Ergen, for his part, has been coy about his next step if he doesn’t win the battle for Sprint. But in an interview in mid-April he dismissed the possibility of partnering with SoftBank in its deal.

“We look at that and say, ‘Why would you want a three-handed deal?’” Mr. Ergen said. “It wouldn’t make sense for us to talk to Softbank. They bring money but they are not the only people who have money.”

The real expertise in U.S. wireless lies with Sprint, Mr. Ergen said, so that’s the partner Dish wants.